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Closure of the class of binary generalized linear models in some non‐standard settings
Author(s) -
Neuhaus John M.
Publication year - 2000
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00268
Subject(s) - generalized linear model , closure (psychology) , linear model , hierarchical generalized linear model , simple (philosophy) , mathematics , binary number , class (philosophy) , generalized linear mixed model , quasi likelihood , least squares function approximation , generalized linear array model , property (philosophy) , function (biology) , algorithm , computer science , statistics , artificial intelligence , count data , estimator , philosophy , arithmetic , epistemology , evolutionary biology , economics , market economy , poisson distribution , biology
This paper considers fitting generalized linear models to binary data in nonstandard settings such as case–control samples, studies with misclassified responses and misspecified models. We develop simple methods for fitting models to case–control data and show that a closure property holds for generalized linear models in the nonstandard settings, i.e. if the responses follow a generalized linear model in the population of interest, then so will the observed response in the non‐standard setting, but with a modified link function. These results imply that we can analyse data and study problems in the non‐standard settings by using classical generalized linear model methods such as the iteratively reweighted least squares algorithm. Example data illustrate the results.